A fast matrix-free elasto-plastic solver for predicting residual stresses in additive manufacturing

Process planning for additive manufacturing (AM) today relies heavily on multi-physics, multi-scale simulation. The focus of this paper is on one aspect of AM simulation, namely, part-level elasto-plastic simulation for residual stress and distortion predictions. This is one of the crucial steps in AM process optimization, but is computationally expensive, often requiring the use of large computer clusters. The primary bottleneck in elasto-plastic simulation is the repeated solution of large linear systems of equations. While there is a wide range of linear solvers, most cannot exploit the unique structured nature of the mesh underlying AM simulation. Here, we revisit a specific matrix-free solver, namely rigid-body deflated solver that has been successfully deployed for solving large linear elastic problems in such scenarios. The salient feature of this solver is that the stiffness matrix is never assembled, thereby reducing the memory requirements significantly, leading to large computational gains. The objective of this paper is to extend the above solver to elasto-plasticity by efficiently updating the element tangent stiffness matrices, and the corresponding deflation matrix. The performance of the proposed method is evaluated on a benchmark problem using multi-core CPU and GPU architectures, and compared against ANSYS. Then, part-level residual stresses and distortion are predicted using the proposed solver. The present work is restricted to associative plasticity with von-Mises yield criteria, but can be extended to other plasticity models.